Cambridge United's Josh Coulson, right, celebrates scoring the only goal of the game against Plymouth Argyle. Photograph: Paul Redding/Action Images

“We are back,” said the apparently edible message on the yellow cup cakes at Abbey Stadium but they cannot have tasted better than the result. Cambridge United, returning to the Football League after nine years, beat Plymouth Argyle 1-0. Two years ago they marked their centenary in the Conference. In May they could truly celebrate it by beating Gateshead in the play-off final. This, in glorious sunshine, was the next step.

On Friday the game was under threat by rain; 38mm fell across the county and brought a Tesco’s roof down. John Beck could not have arranged things better; their manager in the early 90s soaked the pitch’s corners to hold up long balls. The tactic brought two promotions running and fifth place in the second tier, all but putting them into the first Premiership. After near-terminal administration in 2005 they were entitled to raise their roof at the final whistle on Saturday.

Rupert Brooke, well remembered at this time, would not have believed it. In 1912 he wrote in The Old Vicarage: “For Cambridge people rarely smile, being urban, squat and packed with guile.” The scorer was Josh Coulson, locally born. He is 6ft 2in, a central defender, and “whacked it in” as Ryan Donaldson’s corner was flicked on beyond the hour and the near-post throng. “It was probably more a clearance,” he said, defying the poet with a smile. “You couldn’t write a better script.”

“It was absolutely appropriate,” said Richard Money, the head coach. Coulson is United’s longest-serving player, at 25 in his eighth season, so a newcomer to the Football League. “We set out today to try to prove we are good enough to be where we are and we’ve done so. Now we have to prove it over 20 games.” Money talks in football, obscenely at Fifa and in the Premier League. Richard does not waste words. When he said: “We hope to grow together,” he declined the fatuously popular addition of “going forward”.

Guile was in short supply from both sides. “It was important to feel the emotion but to play with calm,” Money said, and Adam Cunnington could have made it easier if he had converted an early penalty when Carl McHugh handled a cross from Kwesi Appiah heading for Donaldson. Luke McCormick, in blush pink from head to foot, guessed left and right in goal.

Donaldson and Appiah were the pick of United’s attack, Donaldson with winged feet and Appiah with deft movement, once with a feint that floored Curtis Nelson and made room for a shot whose menacing arc might have been imagined from the horns of the cattle grazing outside on Coldham’s Common. This is a ground charmingly approached on foot. Aptly these two forced the corner that produced the goal.

Overall, though, as two 4-4-2 systems found closing down easier than opening up, the game cried out for someone with Euclidean appreciation of space and angles. Plymouth forced early corners but rarely worried Chris Dunn in goal. Cambridge is famous for its Backs and all four stood firm, with bodies to the breach when called for. Plymouth’s shirts promised: “Powered access”. Coulson and Tom Bonner allowed them none.

“We have lots of good possession but can’t find the pass,” said Argyle’s manager, John Sheridan. “Cambridge were organised and strong but the stupid things we do, I don’t know what they’re thinking.” Last season they lay 19th after 13 games but seventh with nine to go. All is not lost. They brought 1,221 fans among the 6,009.

Every season starts with fresh hope and happily Graham Scott had no need for cards until added time, when Plymouth’s substitute Nathan Thomas fouled Luke Chadwick, also just on. Chadwick, a Premier League medal-winner with Manchester United in 2001, helped Cambridge over the line from March and described the win at Wembley as “the best moment of my career”. He is Cambridge-born – not squat but packed with guile and smiling.